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Thin-walled cast alloys are one of the most significant enhancements for automotive applications. This paper aims to evaluate the applicability of the "Generalized Incremental Stress-State dependent damage MOdel" (GISSMO) in modern thin-walled cast alloys. Comprehensive experimental tests are carried out to assess the instability and fracture strains on three thin-walled structure alloys that are commonly used. Numerical studies are conducted on the two most common modeling methods, shell-based and tetrahedral models. The parameters in GISSMO are calibrated using theoretical fitting and the inverse analysis approach. Comparisons of the shell-based and tetrahedral-based models with the test results and shell elements are carried out. The characteristics of the two modeling methods are discussed, including element formulas, extrapolating the hardening curves, and mesh-size dependency. It is evaluated that both modeling methods could be applied to thin-walled cast alloys in satisfying agreement. [ABSTRACT FROM AUTHOR]

Thin-walled cast alloys are one of the most significant enhancements for automotive applications. This paper aims to evaluate the applicability of the “Generalized Incremental Stress-State dependent damage MOdel” (GISSMO) in modern thin-walled cast alloys. Comprehensive experimental tests are carried out to assess the instability and fracture strains on three thin-walled structure alloys that are commonly used. Numerical studies are conducted on the two most common modeling methods, shell-based and tetrahedral models. The parameters in GISSMO are calibrated using theoretical fitting and the inverse analysis approach. Comparisons of the shell-based and tetrahedral-based models with the test results and shell elements are carried out. The characteristics of the two modeling methods are discussed, including element formulas, extrapolating the hardening curves, and mesh-size dependency. It is evaluated that both modeling methods could be applied to thin-walled cast alloys in satisfying agreement.

Summary: In this article, we describe a parallel adaptive mesh refinement strategy for two‐phase flows using tetrahedral meshes. The proposed methodology consists of combining a conservative level‐set method with tetrahedral adaptive meshes within a finite volume framework. Our adaptive algorithm applies a cell‐based refinement technique and adapts the mesh according to physics‐based refinement criteria defined by the two‐phase application. The new adapted tetrahedral mesh is obtained from mesh manipulations of an input mesh: operations of refinement and coarsening until a maximum level of refinement is achieved. For the refinement method of tetrahedral elements, geometrical characteristics are taking into consideration to preserve the shape quality of the subdivided elements. The present method is used for the simulation of two‐phase flows, with surface tension, to show the capability and accuracy of 3D adapted tetrahedral grids to bring new numerical research in this context. Finally, the applicability of this approach is shown in the study of the gravity‐driven motion of a single bubble/droplet in a quiescent viscous liquid on regular and complex domains. [ABSTRACT FROM AUTHOR]

In the present paper, development of the Galerkin Finite Element Method-Kinetic-3 Dimentional (GFEM-KIN-3D) computational code for the calculation of the kinetic parameters is reported. To this end, the static neutron diffusion and corresponding adjoint equations are solved using Galerkin Finite element method in the 3 dimensional geometry. Then, the calculated neutron and adjoint flux distributions are used in the perturbation theory to calculate the effective delayed neutron fraction and mean generation time of the neutrons. There is no benchmark problem that includes the information such as the delayed neutron fraction, prompt and delayed neutron spectrum. Therefore, some problems were designed by the author and the kinetic parameters were calculated for the considered problem. Since the neutron diffusion solver was previously validated against the well-known benchmark problems and the equations of perturbation theory is available, we conclude that if the required information is known, the kinetic parameters will be calculated with high accuracy. The developed GFEM-KIN-3D is applicable to the core calculation of the both hexagonal and rectangular reactor cores.

This paper presents a simple and effective strain smoothing method (the strain-smoothed element method) for 3-node triangular and 4-node tetrahedral solid finite elements. While piecewise constant strain fields are constructed through smoothing domains in previous strain smoothing methods, in the proposed method, linear strain fields are constructed within finite elements using constant strains of neighboring finite elements. When the new strain smoothing method is adopted, the triangular and tetrahedral solid finite elements pass all the basic tests; patch, isotropy and zero energy mode tests, and show improved predictive capability. The formulation of the proposed method is presented in detail. Through various numerical examples, we demonstrate the accuracy improvement achieved. [ABSTRACT FROM AUTHOR]

We present a new accuracy condition for the construction of continuous mass-lumped elements. This condition is less restrictive than the one currently used and enabled us to construct new mass-lumped tetrahedral elements of degrees 2 to 4. The new degree-2 and degree-3 tetrahedral elements require 15 and 32 nodes per element, respectively, while currently, these elements require 23 and 50 nodes, respectively. The new degree-4 elements require 60, 61, or 65 nodes per element. Tetrahedral elements of this degree had not been found until now. We prove that our accuracy condition results in a mass-lumped finite element method that converges with optimal order in the L2-norm and energy-norm. A dispersion analysis and several numerical tests confirm that our elements maintain the optimal order of accuracy and show that the new mass-lumped tetrahedral elements are more efficient than the current ones. [ABSTRACT FROM AUTHOR]

A novel mixed four-node tetrahedral finite element, equipped with nodal rotational degrees of freedom, is presented. Its formulation is based on a Hu-Washizu-type functional, suitable to the treatment of material nonlinearities. Rotation and skew-symmetric stress fields are assumed as independent variables, the latter entering the functional to impose rotational compatibility and suppress spurious modes. Exploiting the choice of equal interpolation for strain and symmetric stress fields, a robust element state determination procedure, requiring no element-level iteration, is proposed. The mixed element stability is assessed by means of an original and effective numerical test. The extension of the present formulation to geometric nonlinear problems is achieved through a polar decomposition-based corotational framework. After validation in both material and geometric nonlinear context, the element performances are investigated in demanding simulations involving complex shape memory alloy structures. Supported by the comparison with available linear and quadratic tetrahedrons and hexahedrons, the numerical results prove accuracy, robustness, and effectiveness of the proposed formulation. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The equivalent domain integral method is a reliable tool for J -integral computation in two- and three-dimensional elastic and elastic-plastic fracture mechanics problems. A variant of this method that is independent of finite element mesh is presented. Finite element solution of a boundary value problem is performed on a mesh composed of arbitrary elements. Nodal results are approximated by the moving least squares method that does not require knowledge of mesh topology. Domain integrals are evaluated on a background mesh of hexahedral elements. The mesh has the polar structure with the refinement towards the crack front. Elements of the background mesh are generated in the coordinate system associated with the crack front and then transformed to the global system. Domain integration for each background element is performed once during computations. Evaluation of J -integral for multiple domains is achieved by multiplication of an element domain integral with multiple domain weight functions. Performance of the proposed algorithm is demonstrated by the examples of three-dimensional cracks using meshes of both hexahedral and tetrahedral elements. [ABSTRACT FROM AUTHOR]

Image-based CPFE modeling involves computer generation of virtual polycrystalline microstructures from experimental data, followed by discretization into finite element meshes. Discretization is commonly accomplished using three-dimensional four-node tetrahedral or TET4 elements, which conform to the complex geometries. It has been commonly observed that TET4 elements suffer from severe volumetric locking when simulating deformation of incompressible or nearly incompressible materials. This paper develops and examines three locking-free stabilized finite element formulations in the context of crystal plasticity finite element analysis. They include a node-based uniform strain (NUS) element, a locally integrated B-bar (LIB) based element and a F-bar patch (FP) based element. All three formulations are based on the partitioning of TET4 element meshes and integrating over patches to obtain favorable incompressibility constraint ratios without adding large degrees of freedom. The results show that NUS formulation introduces unstable spurious energy modes, while the LIB and FP elements stabilize the solutions and are preferred for reliable CPFE analysis. The FP element is found to be computationally efficient over the LIB element. [ABSTRACT FROM AUTHOR]

A numerical dispersion analysis (NDA) of the discontinuous Galerkin finite-element time-domain (DG-FETD) method is presented. Vector basis functions under the NDA are with brick and tetrahedral elements. This NDA shows that there exist both normal and spurious modes in the DG-FETD method. A DG-FETD modeling of transverse electromagnetic (TEM) wave propagation in a parallel waveguide is applied to verify the NDA for zeroth-order vector bases. The effect of wave propagation direction and electrical size of elements on numerical dispersion is investigated. It is shown from the NDA for higher-order interpolatory vector bases that the phase error of normal modes can be significantly reduced by using higher-order bases. [ABSTRACT FROM PUBLISHER]

Intervertebral discs are microstructurally complex spinal tissues that add greatly to the flexibility and mechanical strength of the human spine. Attempting to provide an adjustable basis for capturing a wide range of mechanical characteristics and to better address known challenges of numerical modeling of the disc, we present a robust finite-element-based model formulation for spinal segments in a hyperelastic framework using tetrahedral elements. We evaluate the model stability and accuracy using numerical simulations, with particular attention to the degenerated intervertebral discs and their likely skewed and narrowed geometry. To this end, 1) annulus fibrosus is modeled as a fiber-reinforced Mooney-Rivlin type solid for numerical analysis. 2) An adaptive state-variable dependent explicit time step is proposed and utilized here as a computationally efficient alternative to theoretical estimates. 3) Tetrahedral-element-based FE models for spinal segments under various loading conditions are evaluated for their use in robust numerical simulations. For flexion, extension, lateral bending, and axial rotation load cases, numerical simulations reveal that a suitable framework based on tetrahedral elements can provide greater stability and flexibility concerning geometrical meshing over commonly employed hexahedral-element-based ones for representation and study of spinal segments in various stages of degeneration., Competing Interests: MB was employed by Altair Engineering GmbH. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Fasser, Kuravi, Bulla, Snedeker, Farshad and Widmer.)

Abstract: This paper presents three-level residual-based turbulence models for the incompressible Navier–Stokes equations. Employing the variational multiscale (VMS) framework, the velocity and pressure fields are decomposed into two overlapping hierarchical scales, thereby leading to a system of coupled mixed field problems. The mixed problem at the fine scales is stabilized via a subsequent VMS application that results in a further decomposition of the fine-scale velocity field into level-I and level-II scales. The level-II scales are modeled using higher-order bubble functions that are then variationally embedded in the level-I formulation to stabilize it. The level-I problem is modeled via a second set of bubble functions that are linearly independent of the bubbles employed at level-II. Finally, the resulting level-I fine-scales are variationally embedded in the coarse-scale formulation. This yields a residual-based turbulence model for the larger or coarser-scales. A significant feature of the proposed method is that it results in a concurrent top-down and bottom up two-way nesting of the scales. In addition, the resulting turbulence model does not possess any embedded tunable parameters. Another attribute of the formulation is that the fine scales at every level are driven by the residuals of the Euler–Lagrange equations of the coarser scales at the preceding levels, thereby resulting in a method that is variationally consistent. Various algorithmic generalizations of the method are presented that lead to computationally economic residual-based turbulence models. The proposed telescopic depth in scales approach helps make these models accurate for low order tetrahedral and hexahedral elements, a feature that is facilitated by the higher-order bubble functions over element interiors and it results in an enhanced representation of the fine-scale terms modeling the fine viscous effects. From a computational perspective this method results in easy-to-implement equal-order pressure–velocity elements, and possesses the desirable p-refinement feature. Numerical performance of the method is assessed on turbulent channel flow problems at and . Also presented are the results for turbulent SD-7003 airfoil at and comparison is made with the published experimental data and numerical results. [Copyright &y& Elsevier]

Abstract: In various applications of the advancing front based algorithms, involving complicated three dimensional geometries, the algorithm fails to complete the mesh generation process, as a number of small regions cannot be meshed using the standard procedure. These regions, formed by faces of the current front, are usually disconnected, highly non-convex and cannot be handled with simple actions. A strategy involving different novel and already in use operators is presented in this work, to successfully discretize such regions after the completion of the standard advancing front technique (AFT), in order to improve the robustness of the mesh generation procedure for difficult and complicated geometries. Examples of generated meshes using the proposed methodology are also presented for the validation of the proposed strategy. [Copyright &y& Elsevier]

Abstract: In this paper, numerical characteristics of triangular and tetrahedral MINI-elements are investigated through their application to forging simulation. The theoretical background is taken into account with emphasis on the numerical uncertainty due to the stabilizer, which is adopted for computational efficiency. The effect of the stabilizer is investigated by solving an axisymmetric upsetting process under various different conditions. A backward extrusion process of a cube is simulated using traditional tetrahedral and hexahedral elements assisted by the reduced integration scheme and tetrahedral MINI-elements and the predicted results are compared to show their difference and similarity. A rotor pole cold forging process is also simulated by a forging simulator with both tetrahedral MINI-elements and hexahedral elements capabilities and the predictions are compared with experiments. Hexahedral element capability runs manually while tetrahedral MINI-elements capability runs automatically with the help of an intelligent remeshing technique. It is shown that the tetrahedral MINI-elements capability can give quite accurate solution if assisted by the intelligent remeshing technique even though the tetrahedral MINI-elements itself is not numerically clear. [Copyright &y& Elsevier]

This paper presents a variational multiscale residual-based stabilized finite element method for the incompressible Navier–Stokes equations. Structure of the stabilization terms is derived based on the two level scale separation furnished by the variational multiscale framework. A significant feature of the new method is that the fine scales are solved in a direct nonlinear fashion, and a definition of the stabilization tensor τ is derived via the solution of the fine-scale problem. A computationally economic procedure is proposed to evaluate the advection part of the stabilization tensor. The new method circumvents the Babuska–Brezzi (inf–sup) condition and yields a stable formulation for high Reynolds number flows. A family of equal-order pressure-velocity elements comprising 4-and 10-node tetrahedral elements and 8- and 27-node hexahedral elements is developed. Convergence rates are reported and accuracy properties of the method are presented via the lid-driven cavity flow problem. [ABSTRACT FROM AUTHOR]

Recent progress in high-performance computing architectures enables performance enhancements in many fields. One of the most important applications of this enhancement is surface approximation from a set of points. In this research, we propose a technique for constructing a surface approximating an oriented set of samples that is fully supported on graphical processing units (GPUs). The proposed algorithm follows the implicit characterization framework. The algorithm transforms the input samples into an implicit surface that can be extracted using traditional marching cube techniques. Moreover, our approach benefits from the divide-and-conquer strategy in converting the global Poisson problem formulation into smaller independent subproblems. This division enables parallelization of the solutions of these independent subproblems that can be run completely on a GPU. Additionally, we propose an enhanced mathematical formulation of the Poisson problem using a k-dimensional tree (kd-tree) and tetrahedral quadratic elements such that the input points have a greater contribution in solving the local Poisson problems. Finally, we present experiments that demonstrate the efficiency of our proposed approach. [Display omitted] • Recent progress in HPC architectures of GPUs enables performance enhancements in many fields. • The proposed algorithm approximates a surface of an oriented samples, and is fully supported on GPUs. • The algorithm exploits a GPU to construct a kd-tree and enables local tetrahedral decomposition. • The proposed approach outperforms the CPU- and GPU-based related techniques and enhances the quality. [ABSTRACT FROM AUTHOR]

A three-dimensional hybrid immersed smoothed point interpolation method (3D HIS-PIM) has been developed to handle fluid-structure interactions (FSI) with simple geometries. Incompressible viscous fluid is solved by semi-implicit characteristic-based split method with standard Galerkin discretization, smoothed point interpolation method is employed to solve the motion and deformation of nonlinear solids based on gradient smoothing technique, and the virtual fluid is introduced into the entire solid domain to calculate the FSI force. The proposed method can avoid the fluid mesh adjustments, and allows the use of four-node tetrahedral elements for both fluid and solid domains to simplify the pre-processing for mesh generations. The FSI force condition is imposed with a hybrid force, which uses a form of body force for pressure term and boundary force for shear force. The boundary force accords with the physical law and the body force can ensure the numerical stability. The proposed method works well for FSI problems with moving or largely deformable solids, and can achieve more accurate results using a hybrid force than the fully body force in the original method. A large range of mesh size ratios between fluid and solid meshes is allowed due to the treatment of FSI boundary conditions. • Four-node tetrahedral elements are used for both fluid and solid domains. • A hybrid force is used to impose fluid-structure interaction (FSI) force condition. • A large range of mesh size ratios is allowed by the treatment of FSI boundary conditions. • The proposed method works well for three-dimensional FSI problems. [ABSTRACT FROM AUTHOR]

The article examines the computational performance of the nodal spectral element method (SEM) for tetrahedral grids in the context of a high-performance computing platform. Accordingly, the elemental SEM operator is accelerated by the symmetry-based factorization technique, which results in a reduced number of floating point operations and memory accesses. It cites that the performance evaluation shows that a naive implementation of the algorithm can cause a severe degradation of computational efficiency. Moreover, it suggests two algorithmic modifications, which regain the efficiency of the original, non-factorized operator and recover the asymptotic 9/5 speedup due to factorization.

Novel thin-body architectures with complex geometry are becoming of large interest because they are expected to deliver the ITRS prescribed on-current when semiconductor transistors are scaled into nanometer dimensions. We report on the development of a 3D parallel Monte Carlo simulator coupled to a finite element solver for the Poisson equation in order to correctly describe the complex domains of advanced FinFET transistors. We study issues such as charge assignment, field calculation, treatment of contacts and parallelisation approach which have to be taken into account when using tetrahedral elements. The applicability of the simulator is demonstrated by modelling a 10 nm gate length double gate MOSFET with a body thickness of 6.1 nm. [ABSTRACT FROM AUTHOR]

Spectral element methods on tetrahedra with symmetric collocation points can be accelerated by factorizing the discrete operators according to Hesthaven and Teng [SIAM J. Sci. Comput., 21 (2000), pp. 2352-2380]. While these authors focused on first-order conservation laws, the present paper provides an extension to second-order problems. Though factorization is easily accomplished for planar elements, difficulties arise from the presence of variable metric coefficients in curved tetrahedra. Two approaches are considered to cope with this peculiarity: (i) approximation of the metric terms by collocation projection, (ii) Gauss quadrature based on axisymmetric point sets. The first method achieves a separation of the metric terms such that the discrete operators can be reduced to factorizable standard matrices. As a consequence, the performance is comparable to the planar case, whereas the accuracy is limited by the projection step. The second approach maintains accuracy since all terms are evaluated individually in the quadrature points. Nonetheless, complete factorization is achieved by exploiting the symmetry in the quadrature points. Performance analysis shows that the curved element operator is less than three times as costly as the planar element counterpart. [ABSTRACT FROM AUTHOR]

Abstract: In this work finite element simulations are conducted based on the micro structure of polymers in order to transfer the information of the micro level to the macro level. The micro structure of polymers is characterized by chain-like macromolecules linked together at certain points. In this way an irregular three-dimensional network is formed. Many authors use the tool of statistical mechanics to describe the deformation behaviour of the entire network. Most of these concepts can be reformulated as traditional continuum mechanical formulations. They are, however, restricted to affine deformation, regular chain arrangements and purely elastic material behaviour. For this reason, in the present contribution, we propose a new finite element-based simulation method for polymer networks which enables us to include non-affinity and arbitrary chain configurations. It can be easily extended to include chain breakage and reconnection. The polymer structure to be investigated, e.g. a rubber boot or a seal, is discretized by means of tetrahedral elements. To each edge of a tetrahedral element one truss element is attached which models the force–stretch behaviour of a bundle of polymer chains. Each of these tetrahedral unit cells represents the micro mechanical material behaviour in a certain point of the network. The proposed method provides the possibility to observe how changes at the microscopic level influence the macroscopic material behaviour. Such information is especially valuable for the polymer industry. [Copyright &y& Elsevier]

Especially filled rubberlike materials exhibit distinct stress-softening phenomena under cyclic loading commonly known as the Mullins effect. This effect is often explained by chain breakage inside the material which is simulated in the present contribution by an innovative approach. Special finite element unit cells are defined consisting of one tetrahedral element and six truss elements. Putting arbitrary configurations of such unit cells randomly together allows us to simulate complex structures of unfilled elastomers. Filler particles are added by replacing a certain part of the tetrahedrons by linear-elastic material (the filler material). In this way, the increase in stiffness and strength of the composite material is accounted for. Based on comparisons with experimental results, the breakage and reformation of polymer chains is simulated. A satisfactory correlation is obtained between the numerical results and experimental data, also for the large strain regime. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the adaptive finite element solution of a general class of variational problems in three dimensions using a combination of node movement, edge swapping, face swapping and node insertion. The adaptive strategy proposed is a generalization of previous work in two dimensions and is based upon the construction of a hierarchy of locally optimal meshes. Results presented, both for a single equation and a system of coupled equations, suggest that this approach is able to produce better meshes of tetrahedra than those obtained by more conventional adaptive strategies and in a relatively efficient manner. [Copyright &y& Elsevier]

A framework for the construction of stable spectral methods on arbitrary domains with unstructured grids is presented. Although most of the developments are of a general nature, an emphasis is placed on schemes for the solution of partial differential equations defined on the tetrahedron. In the first part the question of well-behaved multivariate polynomial interpolation on the tetrahedron is addressed, and it is shown how to extend the electrostatic analogy of the Jacobi polynomials to problems beyond the line. This allows for the identification of nodal sets suitable for polynomial interpolation within the tetrahedron and, subsequently, for the formulation of stable spectral schemes on such unstructured nodal sets. The second part of this work is devoted to a discussion of weakly imposed boundary conditions, and energy-stable schemes are formulated for a wide class of problems, exemplified by advection problems, advection-diffusion problems, and linear symmetric hyperbolic systems. Finally, in the third part, issues related to computational efficiency and implementation of the schemes are discussed. The spectral accuracy of the approximation is confirmed through an example, and factorization methods for the efficient computation of derivatives on the general nodal sets within the d-simplex are developed, ensuring that the proposed schemes are competitive with tensor- product-based methods. In this last part we also show that the advective operator results in an O(n-2) restriction on the time-step, similar to that of spectral collocation methods employing a tensor-product-based approximation. The performance of the proposed scheme is illustrated by solving a wave problem on a triangulated domain, confirming the expected accuracy and stability. [ABSTRACT FROM AUTHOR]